# FOM: Arithmetic vs Geometry : Categoricity

Kanovei kanovei at wminf2.math.uni-wuppertal.de
Fri Oct 9 02:29:16 EDT 1998

There is a point not properly attended by NT.
He basically argues that
1) Measuring angles with enough precise
we shall always have some small \epsilon of
difference from the exact \pi=180,
hence there is a problem to find that theoretical
geometry which explains this \epsilon most
effectively,
2) Counting objects, we always have an exact result
which does not depend on the type of objects, their, say,
colour or shape, do we use computer or, say, fingers
to count, et cetera.
In other words, physical counting is claimed to be
in 1-1 precise correspondence with mathematical
counting, in opposite to 1) above (on geometry).

However is 2) that true ?
Let's count a collection C of enough many objects
using a counting device D. By Quantum Mechanics,
objects in C will necessarily appear or disappear
with some non-0 probability, and D will have
similar problems, so, basically, is it at all
physically sound to claim that a big enough C
has a certain number of objects ?
If it is not then 2) becomes questionable.

V.Kanovei